The Center for Science and Technology Studies at Leiden University advocates the use of specific normalizations for assessing research performance with reference to a world average. The Journal Citation Score (JCS) and Field Citation Score (FCS) are averaged for the research group or individual researcher under study, and then these values are used as denominators of the (mean) Citations per publication (CPP). Thus, this normalization is based on dividing two averages. This procedure only generates a legitimate indicator in the case of underlying normal distributions. Given the skewed distributions under study, one should average the observed versus expected values which are to be divided first for each publication. We show the effects of the Leiden normalization for a recent evaluation where we happened to have access to the underlying data.